One of the basic characteristics of every living system is the ability to respond to extracellular signals. This is carried out through a limited number of protein-based signaling networks, whose function is not based only on simple transmission of the received signals, but incorporates the processing, encoding and integration of both external and internal signals. The results than lead to different changes in gene expression and regulate cell growth, mitogenesis, differentiation, embryo development, and stress responses in mammalian cells, whereas the malfunction is in correlation with diseases such as cancer, asthma and diabetes. In signaling networks, the basic units are covalent modification cycles, which comprise the activation and deactivation of proteins by other proteins. Protein modification in cell signaling – typically a phosphorylation and dephosphorylation – is a general mechanism responsible for the transfer of a wide variety of chemical signals in biological systems. Although the concept does not seem to be complex from a biochemical point of view, these simple systems can nevertheless provide a large diapason of dynamical responses and are therefore ubiquitous building blocks of signaling pathways. These cycles are often linked, forming multiple layers of cycles, the so-called cascades. Commonly observed instance of signal transduction through a series of protein kinase reactions are the kinases of the mitogen-activated protein kinase (MAPK) cascades. These pathways, which are found in almost all eukaryotes, play an important role in controlling different cellular processes, including fundamental functions. The activation of the cellular response by MAPK pathways typically involves at least three phosphorylation steps. In order to better understand the nature of this regulation and to gain greater insight into the mechanisms that determine the function of cells, signaling modules have been intensively studied using mathematical modeling and computational simulations, through the fast growing field of systems biology and its disciplines. The primary aim is to faithfully describe the system and to be able to predict the system behavior. Synergistically with experimental analysis, the reported observations have allowed one to identify properties of these pathways, such as fast signal propagation, large amplification, short signal duration and noise resistance. Since biochemical parameters in signaling pathways are not easily accessible experimentally, it is necessary to use advanced mathematical tools for their correct estimation. Using the paradigm of man-made optimal signal transduction systems, we chose to take the research path for discovering optimal design of cellular signaling modules. To approach the main thesis objective, we first identified the key system parameters through global sensitivity analysis. Comparative analysis of differences and similarities within different system architectures revealed some insights for initial parameter classification and starting point for optimal system design. In order to be able to interpret a broader range of phenotypes, we take into account both steady-state and dynamic properties simultaneously. Furthermore, we investigated the trade-offs between optimal characteristics. As a result, we found the biochemical and biophysical parameters that determine these trade-offs and we analyzed if there exist conditions under which we can simultaneously achieve optimal steady-state and dynamic performance. We first analyze what are the design principles that lead the system to have the minimal signaling times, subject to a certain level of amplification gain. In this setup, we bring out our main research question: are there any trade-offs and interplay between different steady-state and dynamic properties? Furthermore, we include the property of ultrasensitivity and eventually solve multi-objective optimization problems. A particularly insightful finding of this work is that, upon judicious selection of the kinetic parameters, a simple covalent modification cycle is able to meet multiple objectives simultaneously. In particular, this analysis may help explain why signaling cycles are so ubiquitous in cell signaling. The enhancement of ultrasensitivity and faster signal propagation in the multicyclic systems clearly show the advantages of the natural choice of designing signaling pathways in the form of signaling cascades. The thesis concludes with the potential research steps that could be taken along the same path, and that would gather more quantitative knowledge about signaling pathways.